Time‐dependent finite element simulations of a shear‐thinning viscoelastic fluid with application to blood flow

A new finite element method is developed to simulate time‐dependent viscoelastic shear‐thinning flows characterized by the generalized Oldroyd‐B model. The focus of the algorithm is improved stability through a free‐energy dissipative scheme by using low‐order piecewise‐constant finite element approximations for stress. The algorithm is further modified by incorporating a pressure‐projection method, a DG‐upwinding scheme, a symmetric interior penalty DG method to solve the elliptic pressure‐update equation and a geometric multigrid preconditioner. The improved stability and cost to accuracy is compared when using higher order discontinuous bilinear approximation, where in addition, we consider the influence of a slope limiter for these elements. The algorithm is applied to the 2D start‐up‐driven cavity problem, and the stability of the free energy is illustrated and compared between element choices. An application of the model to modelling blood in small arterioles and channels is considered by simulating pulsatile blood flow through a stenotic arteriole. The individual influences of viscoelasticity and shear‐thinning within the generalized Oldroyd‐B model are investigated by comparing results to the Newtonian, generalized Newtonian and Oldroyd‐B models. Copyright © 2014 John Wiley & Sons, Ltd.     

Self-affinity and nonextensivity of sunspots

In this paper we study the time series of sunspots by using two different approaches, analyzing its self-affine behavior and studying its distribution. The long-range correlation exponent α has been calculated via Detrended Fluctuation Analysis and the power law vanishes to values greater than 11 years. On the other hand, the distribution of the sunspots obeys a q-exponential decay that suggests a non-extensive behavior. This observed characteristic seems to take an alternative interpretation of the sunspots dynamics. The present findings suggest us to propose a dynamic model of sunspots formation based on a nonlinear Fokker–Planck equation. Therefore its dynamic process follows the generalized thermostatistical formalism.     

Integral operators commuting with dilations and rotations in generalized Morrey-type spaces

We find conditions for the boundedness of integral operators $K$ commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of $Kf$ via spherical means of $f$. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others.     

The stabilizability of heat equations with time-dependent coefficients

In this paper, we study the stabilizability of heat equations with time-dependent coefficients. The instability of the systems is illustrated by special solutions. The boundary feedback stabilization results are established by the backstepping method where the growth order of the kernel function depends on time.     

Roe‐type Riemann solvers for general hyperbolic systems

We present a Roe‐type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. We show applications to the compressible Euler equations with general equation of state. An alternative version of the method uses directly the eigenvectors in the averaging process, simplifying the algorithm. These new solvers are applied in conservative and path‐conservative schemes with high‐order accuracy and on unstructured meshes. Copyright © 2014 John Wiley & Sons, Ltd.     

Self-propulsion of flapping bodies in viscous fluids: Recent advances and perspectives

Flapping-powered propulsion is used by many animals to locomote through air or water. Here we review recent experimental and numerical studies on self-propelled mechanical systems powered by a flapping motion. These studies improve our understanding of the mutual interaction between actively flapping bodies and surrounding fluids. The results obtained in these works provide not only new insights into biolocomotion but also useful information for the bio-mimetic design of artificial flyers and swimmers.     

HZ associated production with decay in the Alternative Left-Right Model at CEPC and future linear colliders

In this study, Higgs and Z boson associated production with subsequent decay is attempted in the framework of alternative left-right model, which is motivated by superstring-inspired E_6 model at CEPC and future linear colliders. We systematically analyze each decay channel of Higgs with theoretical constraints and latest experimental methods. Due to the mixing of scalars in the Higgs sector, charged Higgs bosons can play an essential role in the phenomenological analysis of this process. Even though the predictions of this model for the signal strengths of this process are close to the standard model expectations, it can be distinct under high luminosity.     

A vertex‐centered linearity‐preserving discretization of diffusion problems on polygonal meshes

This paper introduces a vertex‐centered linearity‐preserving finite volume scheme for the heterogeneous anisotropic diffusion equations on general polygonal meshes. The unknowns of this scheme are purely the values at the mesh vertices, and no auxiliary unknowns are utilized. The scheme is locally conservative with respect to the dual mesh, captures exactly the linear solutions, leads to a symmetric positive definite matrix, and yields a nine‐point stencil on structured quadrilateral meshes. The coercivity of the scheme is rigorously analyzed on arbitrary mesh size under some weak geometry assumptions. Also, the relation with the finite volume element method is discussed. Finally, some numerical tests show the optimal convergence rates for the discrete solution and flux on various mesh types and for various diffusion tensors. Copyright © 2015 John Wiley & Sons, Ltd.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.